Rooting is getting full control of your device (kinda like admin access). Once youre rooted you can do fun stuff like install custom ROMs, and run apps which require root access to do stuff you cant normally do with your phone (e.g. screen capture apps, accessing the phone's internal storage, uninstall system apps).

Check the sticky at the top of this subforum, it has links to threads which tell you exactly what you need to know and what to do.